1. Field of the Invention
The invention relates to the field of spatial, continuous surfaces having spinning and other dynamic properties which may be used in a multiplicity of educational, utilitarian and ornamental applications.
2. Description of the Prior Art
The use of a Mobius strip for multiple uses is well known. Lamlee, xe2x80x9cMethod of Making a Hexaflexagon,xe2x80x9d U.S. Pat. No. 4,240,858 (1980) describes in FIG. 1 a sheet 10 of stock material which may be card stock, cardboard, plastic, PVC, PVA, acetate or any of thin, opaque or transparent material which is relatively rigid. FIG. 5 shows coated strips comprised of a sandwich 35 that has been cut into strips 42. These strips are comprised of triangular sections 44 of sheet stock covered on both sides by a transparent material. FIG. 7 illustrates a chain 55 comprised of 19 triangles. Beginning with hinge 56 and continuing along hinges 58, 60, 62, 64, 68, 70 and 72, the strip is twisted in one direction and folded onto itself to produce strip 73 shown in FIG. 8. Strip 73 is then folded along hinge 74 to produce the strip configuration 76 shown in FIG. 9. Triangle 84 is folded into position between triangle 83 and 81 and triangles 81 and 84 are glued together. The resulting structure is depicted in FIG. 10. Six of the triangular sections 86 comprising the strip of FIGS. 5 and 7 are then arranged in a side-by-side form of hexagon.
At column 3, beginning at line 50, Lamlee states that the strip portion comprising triangles 79, 80 and 81 are folded under triangle 82 along hinge 78. Triangle 84 is then folded to a position between triangles 83 and 81 and triangles 81 and 84 are adhered together. The resulting structure is shown in FIG. 10. The Lamlee device is actually nothing more than a flattened Mobius strip.
Lehr, xe2x80x9cTherapeutic Elbow Support Method,xe2x80x9d U.S. Pat. No. 5,624,388 (1997) shows in connection with FIG. 2, a device 1 comprised of a loop of elastic material. Loop has a 360xc2x0 twist built into it in order to provide a distinct first surface 2 and a second surface 3. The device of FIG. 2 is similar to a Mobius strip, however, the strip is twisted 360xc2x0 as opposed to 180xc2x0 as in the Mobius strip. As shown on FIG. 2, device 1 will form a figure eight shape which divides the loop into an upper band 5 and lower band 6. The upper and lower band intersect at a cross over point 7.
Bailey, xe2x80x9cModified Helicoidal Wind Responsive Devicexe2x80x9d U.S. Pat. No. 4,850,798 (1989) describes the three dimensional surface formed like two line segments positioned at right angles with respect to another which rotate one about the other on an axis while simultaneously moving along the axis line. The generation of the conventional regular helicoid is shown in FIG. 5. FIG. 4 illustrates a wind-responsive device 10 having a modified helicoidal structure. The device, which is intended primarily to be used as a decoration, is suspended at its upper end from a swivel 20 connected to an eyelet 22 permitting free rotation structure. The embodiment shown in FIG. 1 comprises devices 10A and 10B arranged along a common axis and commonly connected at their upper end. FIG. 6 shows an attachment of sections 10A and 10B with their reinforced section oppositely extending. The greatest visual effect of the two sections are when they have different contrasting colors.
Rodriguez-Perazza xe2x80x9cLink Chain for Power Drives,xe2x80x9d U.S. Pat. No. 4,270,907 (1981) shows in FIG. 3 an endless an standard link chain 300 which includes 25 links 301-325 which are coupled together with a quarter turn twist given to the chain before forming it into a closed loop. The chain drive therefore is an endless chain with a quasi-Mxc3x6bius twist. By doing so, each link 301-325 engages as an adjacent link with an average of 86.4xc2x0 which turns out to have an advantage for gear engagement. If my visualization of the geometry is correct, this is a conventional Mxc3x6bius twist or Mxc3x6bius twist with two series twists.
Molenaar, xe2x80x9cPinwheel,xe2x80x9d U.S. Pat. No. Des. 253,776 (1979) shows that FIGS. 1-7 a conventional pinwheel designed to be ornamental and rotated the wind.
Hornblad, et al. xe2x80x9cMxc3x6bius Strip and Display Utilizing the Same,xe2x80x9d U.S. Pat. No. 4,640,029 (1987) which shows in FIG. 1 a loop which in first appearance is in fact a conventional Mxc3x6bius strip. Both clockwise and counter clockwise Mxc3x6bius strips exist depending on whether the end of an ordinary loop is turned clockwise or counter clockwise in joining it together with opposing end to form the Mxc3x6bius strip. The strip shown in FIG. 1 happens to be clockwise Mxc3x6bius strip, which may give you some momentary confusion if you have to compare it against the model of a counter clockwise Mxc3x6bius strip.
Greeson, xe2x80x9cMxc3x6bius Strip Puzzle,xe2x80x9d U.S. Pat. No. 5,324,037 (1994) is actually a counter clockwise Mxc3x6bius strip.
What is needed is a symmetrical three-twist object, with a different geometry from the Mobius strip, which is dynamic in its function and is a spinner.
The invention, the Mamikon Spinner, is an object which is comprised of an elongated strip (whose proportions preferably exceed 6:1) of a thin, rigid or flexible material, whose one end is twisted three times and attached (e.g. sealed, glued, welded) to the other end, to form a symmetric xe2x80x9cthreefoldxe2x80x9d, three-dimensional shape. Mamikon""s spinner is a unique, symmetric, triple twist strip, made by twisting a strip three times while simultaneously turning it in the same direction. The Mamikon spinner has threefold symmetry, a single surface and a single edge. It is three-dimensional and has a defined center axis about which the threefold symmetry is defined.
Geometrically, Mamikon""s spinner is an xe2x80x9cinfinitexe2x80x9d one-sided surface with an outside envelope or edge that is hexagonal in outline and triangular within an inside envelope or edge. It can be made in a left-sided or right-sided, mirror image.
The most important feature of this shape, for various applications, is its ability to spin under the slightest flow of fluid through it (e.g. air, water and other liquid or viscous media). The spinner, if left to fall, will spin in a certain direction keeping its plane of symmetry horizontal. The Mamikon spinner, moreover, has lifting or thrusting properties when rotated and, inversely works as a propeller.
To differentiate the Mamikon spinner from the traditional Mobius strip, notice that the Mobius strip is asymmetrical, cannot be made symmetrical, and thus can not spin. It will tumble or wobble when dropped from a height.
The manufacture of the Mamikon spinner does not follow from the Mobius strip. This is because one may twist a strip three times, then bring the ends together, and glue them; and this will result in an asymmetrical, curly object. While the curly object can be made symmetrical by turning it xe2x80x9cinside out,xe2x80x9d it is not readily apparent how this is to be done.
In other embodiments the Mamikon spinner is a two-twist, four-twist or more, symmetrical object. The spinner, when made with an odd number of twists, is a one-sided and one-edged surface, but the spinner with even number of twists is a two-sided and two-edged surface. This topologically confirms that the spinner cannot be considered topologically equivalent to a Mobius strip, which is one-sided only.
The spinner rotates easily around its axis of symmetry in response to the movement of slight air currents in the direction of its axis of symmetry when hung by its center, but is virtually unaffected by stronger airflows perpendicular to the axis of symmetry.
Its uses include educational activities, toys, garden hangers, ornamental mobiles, or attractive objects, lampshades, fans, pumps, propellers and windmills. It may also be used in artistic and design settings such as jewelry, art and architectural objects. Still further, it can be employed in tools such as grinders, drill heads, chain saws and the like.
Thus, in summary the features of the invention can be listed as including the following:
1. An object having an axis of symmetry for use in a fluid comprising a continuous strip loop having three twists in the same directions, the object rotating about the axis of symmetry in the fluid to either move the fluid, or to be moved by the fluid.
2. The object of paragraph 1 wherein the fluid is a gas.
3. The object of paragraph 1 wherein the fluid is a liquid.
4. The object of paragraph 1 wherein the fluid is a flowable solid.
5. The object of paragraph 1 when such object has twofold or more symmetry.
6. The object of paragraph 1 where the object has fourfold, or more symmetry.
7. The object of paragraph 1 for use as a propeller in combination with a driven shaft having an axis of rotation, wherein the object has its axis of symmetry coupled to the shaft about the axis of rotation and is driven by the shaft to create thrust.
8. The object of paragraph 7 wherein the use as a propeller in combination with the shaft is as a helicopter blade assembly to create lift.
9. The object of paragraph 1 for use as a driven blade assembly in combination with a shaft having an axis of rotation, wherein the object has its axis of symmetry coupled to the shaft about the axis of rotation and drives the shaft when the object is rotated by moving fluid.
10. The object of paragraph 11 wherein the blade assembly is used as a windmill blade assembly.
11. The object of paragraph 1 for use as a driven tool in combination with a rotating shaft having an axis of rotation, wherein the object has its axis of symmetry coupled to the shaft about the axis of rotation and is driven by the shaft, the strip loop having an edge and at least the edge being provided with a cutting surface.
12. The object of paragraph 1 for use as a driven tool in combination with a rotating shaft having an axis of rotation, wherein the object has its axis of symmetry coupled to the shaft about the axis of rotation and is driven by the shaft, the strip loop having an edge and surface, and being composed of rigid material so that the edge and surface provide a processing edge and surface for materials brought into contact therewith.
13. The object of paragraph 12 for use as a driven tool in combination with a rotating shaft where the processing edge and surface provides a grinding action.
14. The object of paragraph 12 for use as a driven tool in combination with a rotating shaft where the processing edge and surface provides a smashing action.
15. The object of paragraph 1 wherein a portion of the object is reflective to provide a sparkling reflecting surface.
16. The object of paragraph 15 wherein the object is combined with a support which allows the object to rotate while being fixed in a position, and wherein the object is used as a garden hanger.
17. The object of paragraph 15 wherein the object is combined with a support which allows the object to rotate while being fixed in a position, and wherein the object is used as jewelry.
18. The object of paragraph 15 wherein the object is combined with a support which allows the object to rotate while being fixed in a position, and wherein the object is used as a visual attractor.
19. The object of paragraph 1 wherein the strip loop has an edge, and an interior portion to the edge, and further comprising a center support coupled to the interior portion of the edge.
20. The object of paragraph 1 wherein the center support coupled to the interior portion of the edge comprises a triangular, cubic, pyramidal or conic fixture attached to the interior portion.
21. The object of paragraph 19 wherein the strip loop has a reflective surface and further comprising a light source mounted in the center support, the center support being arranged and configured to direct at least a portion of light from the light source toward the reflective surface to create a sparkling reflected beam of light.
22. The object of paragraph 21 wherein the beam of light has at least two color components and wherein the reflective surface of the strip loop is provided with a diffracting surface to decompose the beam of light into the color components.
23. The object of paragraph 1 further comprising a release mechanism so that when the object is rotated through the release mechanism, the object may be disconnected therefrom to permit flight.
24. The object of paragraph 1 wherein the strip loop is made of piecewise flat components with low radar cross sections and comprised of low radio-reflective material.
25. The object of paragraph 19 further comprising a triangular center support whereby a spinning architectural design is provided.
26. The object of paragraph 19 further comprising a sound making device coupled to the object, rotation of the object activating the sound making device.
27. The object of paragraph 1 wherein the object is configured to be used as a manipulative for educational geometric activity package.
28. The object of paragraph 1 wherein the object is twisted 2, 4 or more times such that the object is symmetrical and is capable of spinning when fluid flows through it.
29. The object of paragraph 1 wherein the strip is shaped to increase aerodynamic efficiency when the object is spun.
The invention may be better visualized by turning to the following drawings wherein like elements are referenced by like numerals.